Constructions of Partially Balanced Crossover Designs Based on Two and Higher Order Association Schemes

Abstract

Partially balanced crossover designs (PBCODs) are needed in case a balanced design is not possible due to some reasons. Blaisdell and Raghavarao (1980) and Raghavarao and Blaisdell (1985) introduced the concept of PBCODs and gave certain classes of such designs, along with their efficiency factors. The work on the construction of PBCODs was further considered by Aggarwal and Jha (2006), wherein they gave a number of classes of such designs, based on certain partially balanced incomplete block (PBIB) (2) designs and rectangular association scheme. The present work provides some new classes of connected PBCODs based on 2-, 3-, 4-, and general m-associate class association schemes.

AMS Subject Classification:

• primary 62K10
• secondary 05B30

Keywords:

• Crossover designs
• Partially balanced crossover designs
• Partially balanced designs
• Association schemes